What is: Corner Pooling?

Corner Pooling is a pooling technique for object detection that seeks to better localize corners by encoding explicit prior knowledge. Suppose we want to determine if a pixel at location $\left(i, j\right)$ is a top-left corner. Let $f\_{t}$ and $f\_{l}$ be the feature maps that are the inputs to the top-left corner pooling layer, and let $f\_{t\_{ij}}$ and $f\_{l\_{ij}}$ be the vectors at location $\left(i, j\right)$ in $f\_{t}$ and $f\_{l}$ respectively. With $H \times W$ feature maps, the corner pooling layer first max-pools all feature vectors between $\left(i, j\right)$ and $\left(i, H\right)$ in $f\_{t}$ to a feature vector $t\_{ij}$ , and max-pools all feature vectors between $\left(i, j\right)$ and $\left(W, j\right)$ in $f\_{l}$ to a feature vector $l\_{ij}$. Finally, it adds $t\_{ij}$ and $l\_{ij}$ together.